Optimal packings of bounded degree trees

  title={Optimal packings of bounded degree trees},
  author={Felix Joos and Jaehoon Kim and Daniel Kuhn and Deryk Osthus},
  journal={Journal of the European Mathematical Society},
We prove that if $T_1,\dots, T_n$ is a sequence of bounded degree trees so that $T_i$ has $i$ vertices, then $K_n$ has a decomposition into $T_1,\dots, T_n$. This shows that the tree packing conjecture of Gyarfas and Lehel from 1976 holds for all bounded degree trees (in fact, we can allow the first $o(n)$ trees to have arbitrary degrees). Similarly, we show that Ringel's conjecture from 1963 holds for all bounded degree trees. We deduce these results from a more general theorem, which yields… 

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